Wireless power electronics and controls

ABSTRACT

Magnetic-coupling-based wireless power transfer systems and schemes are provided that ensure fast wireless power transfer to charge batteries of electric vehicles (EVs) with high power transfer efficiencies and safety to humans and other animals in or near the EVs. A wireless power transfer system can include a direct 3-phase AC/AC converter with a circuit topology that enables bidirectional power flow. The direct 3-phase AC/AC converter can convert a power input at a low frequency, such as 3-phase 50/60 Hz, into a power output at a high frequency, such as a frequency in a range of 10-85 kHz for wireless power transfer applications.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is a continuation application of U.S.application Ser. No. 15/404,474, filed Jan. 12, 2017, the disclosure ofwhich is hereby incorporated by reference in its entirety, including allfigures, tables, and drawings.

BACKGROUND

Wireless power transfer (WPT) by way of induction, or inductive powertransfer (IPT), is an emerging technology for transferring electricpower in applications ranging from small consumer gadgets toelectrically powered vehicles. One of the biggest advantages of WPT isits ability to transfer power across relatively large distances withoutthe need for physical contact. In addition, WPT is capable of operatingin hazardous environments as it is resistant to chemicals, particulatedebris, and some of the drawbacks of powering or charging via directelectrical connections, such as contact fouling and corrosion. Oneexample of how WPT could be applied is in static and dynamic charging ofelectric vehicles (EVs). For instance, in static vehicle charging,drivers need simply position their vehicle over a charging element andwalk away, without further action. Further examples of WPT applicationsinclude systems for material handling and biomedical implants. Ofparticular importance in these commercial and industrial applications isthat WPT can transfer energy without risks such as electrical sparkingand electric shock.

BRIEF SUMMARY

Although WPT has already proven to be a promising technology, there isstill a need for ways to increase WPT efficiency, increase WPT systemlongevity, and expand WPT's suitability for various applications.Embodiments of the present invention seek to improve upon thesedeficiencies of the prior art.

Embodiments of the present invention include direct three-phase ac-acmatrix converters for inductive power transfer (IPT) systems withsoft-switching operation. Embodiments of the present invention alsoinclude methods of operation for three-phase ac-ac matrix converters.Embodiments of the present invention can have increased reliability andextended lifetime due to the soft-switching operation and elimination ofshort life electrolytic capacitors. Converters according to anembodiment of the present invention can also reduce switching stress,switching loss and electromagnetic interference (EMI). Embodiments ofthe present invention can operate using a variable frequency controlstrategy based on an energy injection and free oscillation techniquethat is used to regulate the resonant current, the resonant voltage, andthe output power. Converters according to an embodiment of the presentinvention can include reverse blocking switches, allowing for a reducednumber of switches, which consequently increases reliability, increasesefficiency and reduces costs. Embodiments of the present invention caninclude converter control strategies with three different control modes:resonant current regulation control, power regulation control andresonant voltage regulation control. Each of the three different controlmodes can include eight operation modes.

Embodiments of the present invention include a self-tuning sliding-modecontroller for inductive power transfer (IPT) systems based on an analogdesign. A controller according to the present invention canautomatically match the switching operations of power electronicconverters to the resonance frequency of an IPT system. This feature caneliminate or reduce the need for manual frequency tuning. Also, it canenable soft-switching operations (zero-current switching) in powerelectronic converters. According to an embodiment of the presentinvention, a user-defined output resonant current can be maintained,based on an energy-injection, free-oscillation technique. A controlleraccording to the present invention can be implemented on a conventionalfull-bridge or half-bridge AC/DC/AC converter without a dc-linkcapacitor. Therefore, using a controller according to the presentinvention, converters can be expected to have greater reliability andextended lifetime due to the soft-switching operation and elimination ofshort-life electrolytic capacitors. The soft-switching operation canfurther reduce switching stress, switching loss and electromagneticinterference (EMI) of the converter. Also, a controller according to thepresent invention can have a simple analog design, which enables higherfrequency operation, making it suitable for IPT applications.

Embodiments of the present invention include a simplified self-tuningsliding mode control (SMC) for inductive power transfer (IPT) systems.Embodiments can be designed based on an amplitude modulation techniquefor resonant converters and can regulate resonant current around auser-defined reference current. Embodiments of the present invention cansynchronize switching operations of power electronic converters to theresonance current of the IPT system, which in turn eliminates the needfor manual frequency tuning and maximizes extractable power andefficiency. In addition, it enables soft-switching operations(zero-current switching) which increase the efficiency and reliability,and reduce switching stress and electromagnetic interference (EMI) ofthe power electronic converters. Furthermore, embodiments can befabricated with an efficient (or simplified) design, and can beimplemented for different types of converter topologies, includingconventional full-bridge and half-bridge AC/DC/AC converters. Moreover,having an efficient design reduces cost by eliminating expensive digitalcontrollers and enables higher frequency operation, making it suitablefor IPT applications. Experimental studies of an SMC according to anembodiment of the present invention have shown effective regulation ofresonant current around a desired value, synchronization of switchingoperations with resonant current, and enablement of soft-switchingoperations.

Embodiments of the present invention include a self-tuning controllerfor multi-level contactless electric vehicle (EV) charging systems basedon inductive power transfer (IPT). In an embodiment, multi-levelcontactless charging (e.g., consisting of 11 user-defined charginglevels) can be achieved by controlling the energy injection frequency ofthe transmitter coil of an inductive power transfer (IPT) system. Acontroller according to an embodiment of the present invention canself-tune the switching operations to the natural resonance frequency ofthe IPT system and benefit from soft-switching operations (zero-currentswitching), which enhances IPT system performance. Embodiments of thepresent invention can benefit from a simplistic (or efficient) designthat can be implemented based on an analog control circuit.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a typical loosely coupled IPT system.

FIG. 2 shows a three-phase ac-ac matrix converter according to anembodiment of the present invention.

FIG. 3 shows a conceptual plot of three phase input voltages, resonantcurrent and corresponding switching signals of a converter in differentoperation modes, according to an embodiment of the present invention.

FIG. 4 shows current paths of eight modes of operation in a converter,according to an embodiment of the present invention.

FIG. 5 shows an IPT model and its components according to an embodimentof the present invention as simulated using computer software.

FIG. 6 shows the efficiency of a converter according to an embodiment ofthe present invention versus frequency (f_(sw)) and resonant current(i_(r)), calculated analytically.

FIG. 7 shows simulation results of an IPT system according to anembodiment of the present invention with i_(ref)=282.8 A.

FIG. 8 shows the frequency spectrum of the resonant current, accordingto an embodiment of the present invention, shown in FIG. 6.

FIG. 9 is an image of a working prototype IPT system with circular powerpads according to an embodiment of the present invention.

FIG. 10 shows experimental results of output resonant current andcorresponding switching signals of the working prototype of FIG. 9.

FIG. 11 shows experimental results of input voltage (V_(a)), inputcurrent (i_(a)), and power (P_(a)) for phase A and output resonantcurrent (i_(r)) of the working prototype of FIG. 9.

FIG. 12 is a graph of resonant current versus frequency of the workingprototype of FIG. 9.

FIG. 13 shows graphs illustrating output power and resonant current(with P_(ref)=60 W) of the working prototype of FIG. 9.

FIG. 14 is a diagram of a generic loosely coupled IPT system.

FIG. 15A shows full-bridge converter topology and the equivalent circuitof IPT systems.

FIG. 15B shows half-bridge converter topology and the equivalent circuitof IPT systems.

FIG. 16 shows a conceptual plot of resonant current and inverter outputvoltage based on energy injection and free oscillation technique.

FIG. 17 shows diagrams of sliding control modes for full bridge resonantinverters according to an embodiment of the present invention.

FIG. 18 shows the operation a half-bridge controller according to anembodiment of the present invention.

FIG. 19 shows a sliding mode controller for a full-bridge resonantinverter according to an embodiment of the present invention.

FIG. 20 shows a sliding mode controller for a full-bridge resonantinverter according to an embodiment of the present invention.

FIG. 21A shows simulation results of an IPT system with a full-bridgeconverter topology according to an embodiment of the present invention(iref=40 A, Pout=6.6 kW).

FIG. 21B shows simulation results of an IPT system with a full-bridgeconverter topology according to an embodiment of the present invention(iref=60 A, Pout=14 kW).

FIG. 22 shows experimental IPT system with circular pads as atransmitter and receiver, and a full-bridge AC/DC/AC convertercontrolled by an SMC circuit, according to an embodiment of the presentinvention.

FIG. 23A shows experimental resonant current and energy injectionswitching signals of a full-bridge converter according to an embodimentof the present invention (VLL=10V, iref=3:6 A, Pout=35 W).

FIG. 23B shows experimental resonant current and energy injectionswitching signals of a full-bridge converter according to an embodimentof the present invention (VLL=20V, iref=10 A, Pout=155 W).

FIG. 24 shows a controller with an analog control circuit according toan embodiment of the present invention.

FIG. 25 shows resonant current paths in four modes of operationaccording to an embodiment of the present invention.

FIG. 26 shows experimentally produced waveforms of resonance current andconverter output voltage applying a control method according to anembodiment of the present invention.

FIG. 27 shows resonant current and switching signals in differentcharging levels in a simulated experiment of an embodiment of thepresent invention.

FIG. 28 shows a case study IPT setup consisting of two circulartransmitters and receiver power pads, an AC/DC/AC converter as theprimary converter and a controller according to an embodiment of thepresent invention.

FIG. 29 shows experimental test results of resonant current andswitching signals at different charging levels of an IPT systemaccording to an embodiment of the present invention.

DETAILED DESCRIPTION

A typical configuration of an IPT system is shown in FIG. 1. In aloosely coupled IPT system, the inductive link requires a strongmagnetic field to be created to deliver high power levels over largedistances due to weak coupling of the coils. Achieving this requires theuse of power converters that can generate large currents at highfrequencies, often in the kilohertz range (10-58 kHz). In order togenerate a high-frequency current on the primary side, specific types ofpower converters are employed in IPT systems. Power converters play akey role in the performance of IPT systems. Recent developments in IPTsystems have heightened the need for high-power, reliable and efficientconverters. Normally, these converters take 50/60 Hz current and convertto high-frequency using an ac-dc-ac two-stage power conversion. Thepower source of an IPT system is usually the electric utility(single-phase or three-phase) supplying power at 50/60 Hz.

Voltage-source inverters (VSI) based on pulse width modulation (PWM)with a front-end rectifier have become the preferred choice for mostapplications. This is mainly due to their simple topology and low cost.On the other hand, this two-stage topology has low-frequency harmonicson the dc link and the ac input line, which requires the use of verybulky short-life electrolytic capacitors for the dc link and a largelow-pass filter at the output. Several topologies have been proposed tosolve the problems of the traditional ac-dc-ac power converters. Matrixconverters are the main alternatives for two-stage converters. Matrixconverters can convert energy directly from an ac-source to a load withdifferent frequencies and amplitudes, without the need for energystorage elements. These converters have the advantages of simple andcompact topology, bidirectional power flow capability, high-qualityinput-current waveforms, and adjustable input power factors independentof the load.

Various converter topologies have been proposed for different IPTapplications. However, many of the related art topologies suffer fromdrawbacks, such as current sags around input ac voltage zero-crossings,low efficiency, and high cost. Novel three-phase ac-ac matrix convertersfor IPT systems are presented herein. A matrix topology according to anembodiment of the present invention can be built using seven switches,six of which are reverse blocking switches and one is a regular switch.This application also present novel variable frequency control methodsand strategies. The variable frequency control strategies, which can bebased on energy injection and free oscillation techniques, can beapplied to the converter structures that are taught in this application.Benefits of the converter topologies and variable frequency controlstrategies can include soft-switching operation, high efficiency, areduced number of switches and low electromagnetic interference (EMI).

A three-phase ac-ac converter according to an embodiment of the presentinvention is shown in FIG. 2. In FIG. 2, C represents the primarycompensation capacitor, L is the primary self-inductance and R_(eq) isthe reflected resistance of the load at the secondary to the primarycircuit. A converter according to an embodiment of the present inventioncan consist of six reverse blocking switches and one regular switch(IGBT or MOSFET), which are in parallel with a resonant tank. Areverse-blocking switch can include a series combination of aninsulated-gate bipolar transistor (IGBT) or a metal-oxide-semiconductorfield-effect transistor (MOSFET) with a diode. However, individualswitches with intrinsic reverse-blocking, having the advantage of totallower forward voltage, may also be used to enable the converter tooperate with higher efficiency.

Embodiments of the present invention can include control strategies withthree different control modes: resonant current regulation control,power regulation control and resonant voltage regulation control. Thecontrol modes can be based on zero current switching (ZCS) operation.Since embodiments of the present invention include converters based onthe resonant current zero crossing points, the operating frequency ofthe converter is equal to the resonant current frequency (natural dampedfrequency). Therefore, the operating frequency of a converter can bedetermined by the circuit parameters. In a dynamic IPT system, theprimary and secondary self-inductances are fixed by the track/coilparameters, such as size and number of turns in the coil. In practice,although the primary's position relative to secondary affects the mutualinductance, it generally has a small effect on self-inductances, due tothe inherently large gaps that are present in charging systems such aselectric vehicle (EV) dynamic charging. Therefore, self-inductances ofthe primary (L in FIG. 2) and secondary can be assumed to be constant.This ensures the performance of the converter in dynamic IPT systems.

According to an embodiment of the present invention, each of the threecontrol modes (i.e., the resonant current regulation control, powerregulation control and resonant voltage regulation control) can includeeight operation modes, which are presented in Tables I, II and III. Theoperation modes 1 to 6 are energy injection modes in which energy isinjected to the LC tank, and the operation modes 7 and 8 are freeoscillation modes in which the LC tank continues its resonantoscillation. The transition of different modes of operation occurs atcurrent zero-crossing points. Each mode starts at a resonant currentzero-crossing, and continues for a half cycle until the next resonantcurrent zero-crossing. The operation mode transitions are determinedbased on the state of the circuit, as well as the user-defined referencevalues for the resonant current, the resonant voltage, and the outputpower.

Resonant current regulation plays a key role in the power transferperformance of an IPT system. Since the resonant current amplitude isproportional to the amount of injected energy to the LC tank, theresonant current regulation control can be achieved by continuouslychanging the operation mode of the converter from energy injection modes(increasing the resonant current), and vice versa. Using this strategy,the resonant current can be regulated around a user-defined referencecurrent. This is carried out by comparing the peak output resonantcurrent (i_(p)) to the reference current (i_(ref)) at each currentzero-crossing point. The i_(p) is measured in each half cycle of theresonant current. If i_(p) is negative and its absolute value is lessthan i_(ref)(i_(p)<0 and |i_(p)|<i_(ref)), an energy injection to the LCtank is required for the next half cycle to increase the resonantcurrent.

According to Table I, the converter should enter one of the energyinjection modes 1 to 6, depending on the three-phase input voltages.Moreover, if i_(p) is positive or its absolute value is more thani_(ref) (i_(p)>0 or |i_(p)|>i_(ref)), the converter should enter one ofthe free oscillation modes 7 and 8. A conceptual plot of three-phaseinput voltages, resonant current and corresponding switching signals ofthe converter in different modes of operation is presented in FIG. 3.FIG. 4 illustrates the resonant current path in a converter in 8 modesof operation, according to an embodiment of the present invention. Ineach energy-injection mode, the LC tank terminals are switched betweenthe most positive and the most negative input lines. According to TableI, the switching is performed using six reverse-blocking switches,S_(A1), S_(A2), S_(B1), S_(B2), S_(C1) and S_(C2), which are used toswitch the three-phase input lines to the output during modes 1 to 6,based on the measured input voltages. It should be noted that the energyinjection according to this embodiment occurs in positive half-cycles ofthe resonant current. In free-oscillation modes, the negativehalf-cycles of the resonant current are conducted through the parallelswitch S_(F) (mode 8) and the positive half-cycles of the resonantcurrent are conducted through the intrinsic body diode D_(F) (mode 7).It should be noted that negative half-cycles are always free-oscillationmodes; therefore, S_(F) is switched at the rate of the resonancefrequency. Since the resonant current becomes negative after any modefrom 1 to 7, mode 8 always occurs after any other mode of operation.

The voltage limit in the LC tank and particularly in the compensationcapacitor is of great importance. This voltage limit is governed by theinsulation level of the primary coils/tracks and the voltage rating ofthe compensation capacitor. The voltage regulation control can beachieved using an approach similar to the current regulation controlmode. In the following paragraphs it will be shown that the peakresonant voltage occurs in each resonant current zero-crossing.Therefore, the resonant voltage can be measured in each currentzero-crossing and peak voltage detection is not required.

In voltage regulation control mode, if the peak resonant voltage isnegative and its absolute value is lower than the reference voltage(v_(p)<0 and |v_(p)|<v_(ref)), then according to Table III, the circuitwill enter one of the energy injection modes 1 to 6, depending on thethree-phase input voltages. Therefore, energy will be injected to the LCtank for a half cycle to increase the resonant voltage, and the LC tankterminals are switched between the most positive and the most negativeinput lines. The switching can be performed using six switches, S_(A1),S_(A2), S_(B1), S_(B2), S_(C1) and S_(C2), which are used to switch thethree-phase input lines to the output during modes 1 to 6, according toTable II and based on the measured input voltages. Mode 7 occurs whenthe peak voltage is negative and its absolute value is higher than thereference voltage (v_(p)<0 and |v_(p)|>v_(ref)) and therefore energyinjection to LC tank should be avoided for a half cycle to decrease theresonant voltage. In this mode, the LC tank enters a free oscillationstate and the resonant current is positive, which is conducted throughthe intrinsic body diode (D_(F)) of the parallel switch (S_(F)) for mode7 as shown in FIG. 4. In mode 8, the resonant current is negative andthe switch S_(F) is on. Since the resonant current becomes negativeafter any mode from 1 to 7, mode 8 always occurs after any other mode ofoperation.

TABLE I SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN CURRENTREGULATION CONTROL MODE. Conducting Mode Resonant Current Input VoltagesSwitches 1 ip < 0, |ip| < i_(ref) V_(b) < V_(c) < V_(a) S_(A1), S_(B2) 2ip < 0, |ip| < i_(ref) V_(c) < V_(b) < V_(a) S_(A1), S_(C2) 3 ip < 0,|ip| < i_(ref) V_(a) < V_(c) < V_(b) S_(B1), S_(A2) 4 ip < 0, |ip| <i_(ref) V_(c) < V_(a) < V_(b) S_(B1), S_(C2) 5 ip < 0, |ip| < i_(ref)V_(b) < V_(a) < V_(c) S_(C1), S_(B2) 6 ip < 0, |ip| < i_(ref) V_(a) <V_(b) < V_(c) S_(C1), S_(A2) 7 ip < 0, |ip| > i_(ref) — D_(F) 8 ip > 0 —S_(F)

TABLE II SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN VOLTAGEREGULATION CONTROL MODE. Resonant Voltage Conducting Mode & CurrentInput Voltages Switches 1 vp < 0, |vp| < v_(ref) V_(b) < V_(c) < V_(a)S_(A1), S_(B2) 2 vp < 0, |vp| < v_(ref) V_(c) < V_(b) < V_(a) S_(A1),S_(C2) 3 vp < 0, |vp| < v_(ref) V_(a) < V_(c) < V_(b) S_(B1), S_(A2) 4vp < 0, |vp| < v_(ref) V_(c) < V_(a) < V_(b) S_(B1), S_(C2) 5 vp < 0,|vp| < v_(ref) V_(b) < V_(a) < V_(c) S_(C1), S_(B2) 6 vp < 0, |vp| <v_(ref) V_(a) < V_(b) < V_(c) S_(C1), S_(A2) 7 vp < 0, |vp| > v_(ref) —D_(F) 8 ip > 0 — S_(F)

TABLE III SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN POWERREGULATION CONTROL MODE. Output Power & Conducting Mode Resonant CurrentInput Voltages Switches 1 P_(out) < P_(ref), ip < 0 V_(b) < V_(c) <V_(a) S_(A1), S_(B2) 2 P_(out) < P_(ref), ip < 0 V_(c) < V_(b) < V_(a)S_(A1), S_(C2) 3 P_(out) < P_(ref), ip < 0 V_(a) < V_(c) < V_(b) S_(B1),S_(A2) 4 P_(out) < P_(ref), ip < 0 V_(c) < V_(a) < V_(b) S_(B1), S_(C2)5 P_(out) < P_(ref), ip < 0 V_(b) < V_(a) < V_(c) S_(C1), S_(B2) 6P_(out) < P_(ref), ip < 0 V_(a) < V_(b) < V_(c) S_(C1), S_(A2) 7P_(out) > P_(ref), ip < 0 — D_(F) 8 ip >0 — S_(F)

In dynamic IPT systems, due to inherent variations in the load, powertransfer control is important. The power input regulation control can beachieved using an approach similar to current regulation control method.The peak current (i_(p)) and the input voltage (V_(in)) are measured.Considering that all negative half-cycles are free oscillation modes,and in free oscillation modes the input voltage is zero (V_(in)=0), theaverage output power (P_(in)) for a full-cycle (T) can be calculated asbelow:

$\begin{matrix}{P_{out} = {{\int_{T}{i_{p}V_{in}}} = {\frac{1}{\pi}i_{p}V_{in}}}} & (1)\end{matrix}$

In this control mode, in each current zero crossing P_(out) is comparedto a reference power (P_(ref)) and if the average output power (P_(out))in one half cycle is lower than the reference power (P_(ref)), thecircuit will enter one of the energy injection modes 1 to 6, dependingon the three-phase input voltages based on Table III. Therefore, energywill be injected to the LC tank in the next half cycle to increase theresonant current, and the LC tank terminals are switched between themost positive and the most negative input lines. According to Table III,the switching is performed using six switches, S_(A1), S_(A2), S_(B1),S_(B2), S_(C1) and S_(C2), which are used to switch the three-phaseinput lines to the output during modes 1 to 6, based on the measuredinput voltages. Mode 7 occurs when the average output power (P_(out)) ishigher than the reference power (P_(ref)); therefore, energy injectionto LC tank should be avoided for a half cycle to decrease the resonantcurrent. In this mode, the LC tank enters a free oscillation state andthe resonant current is positive, which is conducted through theintrinsic body diode (D_(F)) of the parallel switch (S_(F)) for mode 7,as shown in FIG. 4. In mode 8, the resonant current is negative and theswitch S_(F) is on. Since the resonant current becomes negative afterany mode between 1 to 7, mode 8 always occurs after any other mode ofoperation.

A theoretical analysis of converter topologies and modes of operationwill now be discussed. The differential equation of a LC tank with aprimary self-inductance of L, and a compensation capacitor C with anequivalent resistance of R can be expressed as:

$\begin{matrix}{{{L\frac{di}{dt}} + {R_{eq}i} + {\frac{1}{C}{\int_{0}^{t}{idt}}} + {v_{a}(0)}} = V_{t}} & (2)\end{matrix}$

where i is the resonant current, v_(c) is the voltage of thecompensation capacitor and V_(t) is the input voltage. Equation (2) canbe rewritten as the following second order differential equation:

$\begin{matrix}{{\frac{d^{2}i}{{dt}^{2}} + {\frac{R_{eq}}{L}\frac{di}{dt}} + {\frac{1}{LC}i}} = 0} & (3)\end{matrix}$

where the initial conditions of the circuit are:

$\begin{matrix}{{{i(0)} = 0}{L\frac{di}{dt}(0)} = {V_{t} - {v_{c}(0)}}} & (4)\end{matrix}$

The solution of (3) based on initial conditions in (4) is derived as:i=Ke ^(−t/τ) sin(ωt)  (5)

where the natural damped frequency ω=√{square root over (ω₀ ²−α²)},resonant frequency ω₀=1/√{square root over (LC)}, damping coefficientα=R_(eq)/2L, damping time constant τ=2L/R, and the coefficient K isexpressed as:

$\begin{matrix}{K = \frac{V_{t} - {v_{c}(0)}}{\omega\; L}} & (6)\end{matrix}$

Equation (5) shows that the peak current decreases exponentially with atime constant of τ and (6) shows that the value of K changes in eachhalf cycle depending on the input voltage and initial voltage of thecompensation capacitor. It should be noted that in the free oscillationmodes the input voltage is zero (V_(t)=0). Also, the compensationcapacitor voltage can be expressed as:

$\begin{matrix}{{v_{c}(t)} = {{v_{c}(0)} + {\frac{K\;\tau}{C( {1 + {\tau^{2}\omega^{2}}} )}( {{\tau\omega} - {e^{{- t}/\tau}\lbrack {{\sin( {\omega\; t} )} + {{\tau\omega}\;{\cos( {\omega\; t} )}}} \rbrack}} )}}} & (7)\end{matrix}$

The resonant current and voltage equations (5) and (7) can be used forfinding the peak values of current and voltage in each half cycle. Inorder to find the peak value of the resonant current i_(n), which occursat the time t_(n) corresponding to the nth current peak, the followingequation can be solved to find the extremum points of the resonantcurrent:

$\begin{matrix}{\frac{di}{dt} = {{K\;{e^{{- t}/\tau}\lbrack {{\omega\;{\cos( {\omega\; t} )}} - {\frac{1}{\tau}{\sin( {\omega\; t} )}}} \rbrack}} = 0}} & (8)\end{matrix}$By simplifying (8) the following equations are derived:

$\begin{matrix}{{\tan( {\omega\; t_{n}} )} = {\tau\omega}} & (9) \\{t_{n} = \frac{{{atan}({\tau\omega})} + {n\;\pi}}{\omega}} & (10)\end{matrix}$Therefore, the n^(th) peak value of the resonant current can becalculated using (5) and (10) as the following equation:

$\begin{matrix}{i_{n} = {{{Ke}^{- \frac{{{atan}{({\tau\omega})}} + {n\;\pi}}{\tau\omega}}( {- 1} )}^{n}\frac{\tau\omega}{\sqrt{1 + ({\tau\omega})^{2}}}}} & (11)\end{matrix}$Similarly the peak values of the resonant voltage can be found using (7)as follows:

$\begin{matrix}{\frac{{dv}_{c}}{dt} = {{{- \frac{K\;\tau\; e^{{- t}/\tau}}{C( {1 + {\tau^{2}\omega^{2}}} )}}( {\lbrack {{\omega\;{\cos( {\omega\; t} )}} - {{\tau\omega}^{2}{\sin( {\omega\; t} )}}} \rbrack - {\frac{1}{\tau}\lbrack {{\sin( {\omega\; t} )} + {{\tau\omega}\;{\cos( {\omega\; t} )}}} \rbrack}} )} = 0}} & (12)\end{matrix}$Equation (12) can be simplified by the following set of equations:

$\begin{matrix}{\frac{{dv}_{c}}{dt} = {{\frac{K}{C}e^{{- t}/\tau}{\sin( {\omega\; t} )}} = 0}} & (13) \\{{\sin( {\omega\; t_{n}} )} = 0} & (14) \\{t_{n} = \frac{n\;\pi}{\omega}} & (15)\end{matrix}$

Based on (5), (13), (14) and (15) it can be seen that in each resonantcurrent zero-crossing, resonant voltage is exactly at its peak. Sincethe control modes presented above are all based on resonance currentzero-crossing points, the voltage regulation control mode can beestablished on peak values of resonant voltage in each currentzero-crossing.

Using (5), the resonant current in a time period composed of both energyinjection and free oscillation modes can be expressed as follows:

$\begin{matrix}{{i(t)} = \{ \begin{matrix}{K_{i}e^{{- t}/\tau}{\sin( {\omega\; t} )}} & {0 < t < \frac{\pi}{\omega}} \\{K_{f}e^{{- t}/\tau}{\sin( {\omega\; t} )}} & {\frac{\pi}{\omega} < t < \frac{2\; m\;\pi}{\omega}}\end{matrix} } & (16)\end{matrix}$

where m denotes the number of cycles, which is composed of one energyinjection half cycle and 2m−1 free oscillation half cycles, K_(i) andK_(f) are coefficients of (5) in the first energy injection and freeoscillation half cycles, respectively, and can be calculated using (6)and (7) as follows:

$\begin{matrix}{K_{i} = {\frac{1}{\omega\; L}\lbrack {V_{i} - {v_{c}(0)}} \rbrack}} & (17) \\{K_{f} = {{\frac{1}{\omega\; L}\lbrack {v_{c}( \frac{\pi}{\omega} )} \rbrack} = {\frac{1}{\omega\; L}\lbrack {{v_{c}(0)} + {\frac{K_{i}\tau^{2}\omega}{C( {1 + {\tau^{2}\omega^{2}}} )}( {1 + e^{{- \pi}/{\tau\omega}}} )}} \rbrack}}} & (18)\end{matrix}$

By assuming i_(ref) as the reference current, using (11) and (12) thenumber of cycles that the next energy injection should occur (m) can becalculated as follows:

$\begin{matrix}{m = {\frac{1}{\pi}\lfloor {{{\tau\omega ln}( \frac{K_{f}{\tau\omega}}{i_{ref}\sqrt{1 + ({\tau\omega})^{2}}} )} + {\arctan({\tau\omega})}} \rfloor}} & (19)\end{matrix}$

Equation (19) predicts the number of cycles in which the LC tank willcontinue its free oscillation mode, after an energy-injection mode, as afunction of initial condition (K_(f)), circuit parameters (τω) and thereference current i_(ref). A duty-cycle can be defined as the ratio ofthe number of energy injection modes to the number of free-oscillationmodes in the time interval between two successive energy injectionmodes, and can be written as follows:

$\begin{matrix}{D_{i} = {\frac{1}{m + 1} = \frac{f_{inj}}{f_{r}}}} & (20)\end{matrix}$

where f_(inj) is the switching frequency of the energy-injection modesand f_(r) is the resonance frequency of the LC tank. The duty-cycleD_(i), is a measure that represents the energy demand for the LC tank.For example, in FIG. 3, this measure is D_(i)=0.5, which shows that onlyhalf of the cycles energy needs to be injected to the LC tank.

A. Converter Loss Analysis

The power loss of a converter according to an embodiment of the presentinvention can be calculated by evaluating the conduction and switchinglosses of the power switches in different modes of operation. The lossof each power switch is composed of switching and conduction losses andcan be written as follows:P _(Sx) =P _(Scon) +P _(Ssw)=[V _(F) I _(avg) +R _(F) I _(rms) ^(2]) T_(con) f _(sw)+[(E _(on) +E _(off))+½C _(oss) V _(in) ^(2]) f_(sw)  (21)

where P_(Scon) and P_(Ssw) are the conduction and switching losses ofthe switch S_(x), respectively, V_(F) is the forward voltage of thepower switch (in power MOSFETs, V_(F)=0), R_(F) is the equivalentresistance of the switch during the on state, I_(avg) and I_(rms) arethe mean and RMS values of the conducted current, respectively, T_(con)is the conduction time of the switch, f_(sw) is the switching frequency,E_(on) and E_(off) are volt-ampere crossover energy losses during theswitch turn-on and turn-off transitions, respectively, C_(oss) is theoutput capacitance of the switch, and V_(in) is the input voltage. SinceZCS switching can always be performed, the switching losses fromvolt-ampere crossover are minimized and thus are relatively low.Therefore, the conduction losses dominate, followed by the losses due toC_(oss) (output losses). The losses associated with any diode in theconverter are composed of conduction and reverse recovery losses and canbe calculated as below:P _(Dx) =P _(Dcond) +P _(Drr) =V _(FD) I _(avg) T _(con) f _(sw) +E_(rr) f _(sw)  (22)

where P_(Dcond) and P_(Drr) are the conduction and reverse recoverylosses of the diode D_(x), respectively, V_(FD) is the forward voltageof the diode and E_(rr) is the reverse recovery energy of the diode. Thelosses of the converter can be determined by calculating the lossesassociated with energy-injection and free-oscillation modes separately,considering the fact that the switching frequency of all the switchesare f_(inj)=D_(ifr), except S_(F) which has switching frequency off_(r). In each energy injection mode (modes 1 to 6) two reverse blockingswitches can be used; therefore, the losses associated with energyinjection modes (P_(in)) can be described as below:P _(inj)=2D _(i)(P _(Sx) +P _(Dx))  (23)

It should be noted that if the switches S_(A1), S_(A2), S_(B1), S_(B2),S_(C1) and S_(C2) can be switches with built-in reverse blockingcapability, P_(Dx) loss is eliminated in (23), and as a result theefficiency of the converter will be increased. Since S_(F) and its bodydiode D_(F) are the only switches involved in free oscillation modes,the losses associated with free oscillation modes (P_(osc)) can becalculated as follows:P _(osc) =P _(Sx) +D _(i) P _(Dx)  (24)

Finally the total dissipated power can be described as follows:P _(loss) =P _(inj) +P _(osc)  (25)

TABLE IV TYPICAL VALUES FOR PARAMETERS USED FOR THEORETICAL CONVERTERLOSS CALCULATION. Parameter Description Typical Value V_(F) Switchforward voltage 1.5 V R_(F) Equivalent ON-state resistance 0.08 ΩC_(oss) Output capacitance 250 pF E_(on) + E_(off) Switching volt-ampere2 mJ crossover energy losses V_(FD) Diode forward voltage 1.8 V E_(rr)Reverse recovery energy loss 200 μJ

Typical values for high power switches and diodes for a 50 A outputcurrent are presented in Table IV. However, for different values ofcurrent, these typical values should be modified accordingly. FIG. 6presents the efficiency of a converter according to an embodiment of thepresent invention versus resonant current and switching frequency, whichis calculated based on Table IV and equations (21)-(25). This figureshows that the efficiency of the converter increases as the resonantcurrent increases, and any change in the switching frequency does notaffect the efficiency significantly in high resonant currents. Accordingto this analysis, the maximum efficiency of the converter can reach96.6%.

FIG. 14 shows a generic IPT system that is composed of power converters,loosely coupled magnetic structures and compensation components. Due toits loose magnetic structure, different control methods for IPT systemsand resonant converters have been proposed. These methods includepower-frequency control, phase-shift and frequency control, loaddetection, power flow control, and sliding mode control (SMC). Controlmethods can have self-tuning capability. This feature makes controllerssuitable for dynamic IPT applications in which the resonance frequencyof the system may have small variations due to load variations on thereceiver side. Furthermore, control methods can have additionalapplications such as energy encryption, wherein the IPT system has avariable resonance frequency and is used with different compensationcapacitors.

One effective method for controlling an IPT system is amplitudemodulation of the resonant current based on an energy injection andfree-oscillation technique. This control technique can be designed forwide range of converter topologies including two-stage AC/DC/AC andsingle-stage matrix converters. This technique has been successfullyemployed in single-phase and three-phase matrix converters toeffectively regulate resonant current. However, the exiting controllersare typically digital and designed based on DSP/FPGA. Since digitalcontrollers have a limited sampling rate and processing speed, they arenot well suited for high-frequency control of IPT systems. On the otherhand, SAE TIR J2954 standard establishes a common frequency band using85 kHz (81.39-90 kHz) for electric vehicle inductive charging systems.Thus, due to high operating frequency requirements of IPT systems, theuse of digital controllers for IPT applications is complex and requireshigh processing speeds, which increases costs.

Embodiments of the present invention include a sliding mode controller(SMC) for inductive power transfer (IPT) systems based on an energyinjection, free-oscillation amplitude modulation technique. Embodimentsof the present invention include a design methodology of an SMC fortwo-stage AC/DC/AC converter topologies. According to an embodiment ofthe present invention, an SMC has self-tuning capability that allows thecontroller to synchronize the switching operations of the powerelectronic converters to the resonant current and enables soft-switchingoperations. According to an embodiment, a simplified SMC is presentedthat eliminates the need for high-cost DSP/FPGA controllers and canoperate at higher speeds than digital controllers, while still havingsignificantly lower costs. Therefore, embodiments of the presentinvention can be suitable for IPT applications in which high operatingfrequencies are required.

FIGS. 15A and 15B show full-bridge and half-bridge converter topologies,respectively. These converters are connected to an equivalent circuit ofan IPT system with a series capacitance C, a primary inductance L, andan equivalent resistance R which represents the reflected load from thesecondary circuit to the primary. The sliding mode control (SMC) can bedesigned based on the energy injection and free-oscillation techniquefor resonant circuits with LC tanks. A plot of resonant current andinverter output voltage is shown in FIG. 16. A seen in FIG. 16, eachhalf-cycle can be either an energy-injection mode or a free-oscillationmode. The transition to different modes only occurs at zero-crossingpoints, which ensures soft-switching operation of the converter. Inenergy-injection modes, energy is injected into the LC tank from the DCvoltage source, thus increasing the resonant current. On the other hand,in free-oscillation modes the LC tank continues its oscillation withoutany energy injection from the DC source, thus decreasing the resonantcurrent. Therefore, resonant current can be regulated around apredefined reference current by constantly switching between these twooperation modes. The state-space equations of an IPT system connected toany of the converters of FIG. 15 can be written as follows:

$\begin{matrix}{{x(t)} = \begin{bmatrix}{v_{c}(t)} \\{i_{l}(t)}\end{bmatrix}} & (26) \\{{{\overset{.}{x}(t)} = {{{Ax}(t)} + {{Bu}(t)}}}{{y(t)} = {{{Cx}(t)} + {{Du}(t)}}}} & (27)\end{matrix}$where v_(c)(t) is the voltage of the capacitor C and i_(l)(t) is theresonant current of the LC tank and:

$\begin{matrix}{{A = \begin{bmatrix}0 & \frac{1}{C} \\{- \frac{1}{L}} & {- \frac{R}{L}}\end{bmatrix}},{B = \begin{bmatrix}0 \\\frac{1}{L}\end{bmatrix}},{C = \lbrack {0\mspace{14mu} 1} \rbrack},{D = 0}} & (28)\end{matrix}$

Assuming that each half-cycle starts at a current zero-crossing, theinitial condition and the input can be written as follows:

$\begin{matrix}{{{x(0)} = \begin{bmatrix}v_{0} \\0\end{bmatrix}},{u = v_{in}}} & (29)\end{matrix}$where v₀ is the initial capacitor voltage and v_(in) is the inputvoltage across the LC tank. The solution to (27) in Laplace domain canbe written as:

$\begin{matrix}{{X(s)} = {( {{sI} - A} )^{- 1}\lbrack {{x(0)} + {B\frac{v_{in}}{s}}} \rbrack}} & (30)\end{matrix}$

Using (28) and (29), (30) can be rewritten as follows:

$\begin{matrix}{{X(s)} = \begin{bmatrix}{\frac{v_{in}}{s( {{CLs}^{2} + {CRs} + 1} )} + \frac{{Cv}_{0}( {R + {Ls}} )}{{CLs}^{2} + {CRs} + 1}} \\{\frac{{Cv}_{in}}{{CLs}^{2} + {CRs} + 1} - \frac{{Cv}_{0}}{{CLs}^{2} + {CRs} + 1}}\end{bmatrix}} & (31)\end{matrix}$

By applying inverse Laplace transform to (31), the time domain solutionx(t) can be written as follows:

$\begin{matrix}{{{x(t)} = {\begin{bmatrix}{v_{in} + {( {v_{0} - v_{in}} ){e^{{- t}/\tau}\lbrack {{\cos( {\omega\; t} )} + {\frac{1}{\tau\omega}{\sin( {\omega\; t} )}}} \rbrack}}} \\{\frac{( {v_{in} - v_{0}} )}{\omega\; L}e^{{- t}/\tau}{\sin( {\omega\; t} )}}\end{bmatrix}\mspace{14mu}{where}}},} & (32) \\{{\omega = \sqrt{\frac{1}{LC} - \frac{R^{2}}{4L^{2}}}},{\tau = \frac{2L}{R}}} & (33)\end{matrix}$

Equation (32) gives the resonant current and voltage for each half-cyclebased on the initial capacitor voltage v₀ and input voltage v_(in). Thehalf-cycles wherein v_(in)=V_(dc) or v_(in)=−V_(dc) are energy-injectionhalf-cycles while the half-cycles wherein v_(in)=0 are free-oscillationhalf-cycles. Using (32), the peak resonant current in each half cyclei_(p), which occurs at the time t_(p) can be found by solving thefollowing equation:

$\begin{matrix}{\frac{{di}_{l}}{dt} = {{\frac{( {v_{in} - v_{0}} )}{\omega\; L}{e^{{- t_{p}}/\tau}\lbrack {{\omega\mspace{14mu}{\cos( {\omega\; t_{p}} )}} - {\frac{1}{\tau}{\sin( {\omega\; t_{p}} )}}} \rbrack}} = 0}} & (34)\end{matrix}$

By simplifying (34), t_(p) can be calculated as follows:

$\begin{matrix}{t_{p} = \frac{\arctan({\tau\omega})}{\omega}} & (35)\end{matrix}$

By substituting (35) in (32), the peak resonant current i_(p) can becalculated:

$\begin{matrix}{i_{p} = {{- \frac{( {v_{in} - v_{0}} )}{\omega\; L}}e^{- \frac{\arctan{({\tau\omega})}}{\tau\omega}}\frac{\tau\omega}{\sqrt{1 + ({\tau\omega})^{2}}}}} & (36)\end{matrix}$

Based on the energy-injection and free-oscillation control technique,the transitions always occur at resonant current zero-crossing points.Therefore, the state-space model presented in (27) can be discretized inorder to simplify the design procedure of the SMC. Thus, the samplingtime T_(s) is defined as:

$\begin{matrix}{T_{s} = \frac{\pi}{\omega}} & (37)\end{matrix}$

The equivalent discretized state-space model given by (27) can berewritten as follows:

$\begin{matrix}{{x\lbrack k\rbrack} = \begin{bmatrix}{v_{c}\lbrack k\rbrack} \\{i_{l}\lbrack k\rbrack}\end{bmatrix}} & (38) \\{{{x\lbrack {k + 1} \rbrack} = {{A_{d}{x\lbrack k\rbrack}} + {B_{d}{u\lbrack k\rbrack}}}}{{y\lbrack {k + 1} \rbrack} = {{C_{d}{x\lbrack k\rbrack}} + {D_{d}{u\lbrack k\rbrack}}}}} & (39)\end{matrix}$where A_(d) and B_(d) can be calculated as follows:A _(d)=

⁻¹{(sI−A)⁻¹}_(t=T) _(s)   (40)B _(d) =A ⁻¹(A _(d) −I)B  (41)

Using (28), (40) and (41) can be simplified as follows:

$\begin{matrix}{A_{d} = \begin{bmatrix}{- e^{{- \pi}/{\tau\omega}}} & 0 \\0 & {- e^{{- \pi}/{\tau\omega}}}\end{bmatrix}} & (42) \\{B_{d} = \lbrack {1 + {e^{{- \pi}/{\tau\omega}}\mspace{14mu} 0}} \rbrack} & (43)\end{matrix}$

Also, based on the discretized model given by (39), the discretized peakresonant current can be rewritten as follows:

$\begin{matrix}{{i_{p}\lbrack k\rbrack} = {( {{u\lbrack k\rbrack} - {x_{1}\lbrack k\rbrack}} )\frac{\tau\; e^{{- {\arctan({\tau\omega})}}/{\tau\omega}}}{L\sqrt{1 + ({\tau\omega})^{2}}}}} & (44)\end{matrix}$

To design an SMC based on energy-injection and free-oscillationtechniques to perform amplitude modulation on resonant current, asliding surface is defined based on the peak resonant current given by(44) as follows:σ[k]=|i _(p)[k]|−i _(ref)  (45)wherein σ[k] is the discrete sliding surface and i_(ref) is thereference current. The reaching law of the SMC can be formulated asfollows:(σ[k+1]−σ[k])σ[k]<0  (46)

TABLE V SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN FULL-BRIDGECONTROLLER. Mode Type sign(i_(r)) sign(σ[k]) S₁ S₂ S₃ S₄ 1 energyinjection 1 1 1 0 0 1 2 energy injection 0 1 0 1 1 0 3 free oscillation1 0 1 0 0 0 4 free oscillation 0 0 0 1 0 0

Using (45) and (46) the following can be derived:(|i _(p)[k+1]|−|i _(p)[k]|)σ[k]<0  (47)

Based on (47) the feedback control law u[k] is picked so that thediscrepancy between consecutive resonant current peaks and σ[k] haveopposite signs. In other words, whenever σ[k]<0, energy injection to theLC tank should be performed to increase the peak resonant current and,whenever σ[k]>0, the LC tank should continue its free-oscillation. In afull-bridge converter as shown in FIG. 15A, the input voltage of the LCtank can be either V_(dc), −V_(dc) or 0. As a result, based on (47), thecontrol law for a full-bridge converter can be derived:

$\begin{matrix}{{u\lbrack {k + 1} \rbrack} = \{ \begin{matrix}V_{dc} & {{{\sigma\lbrack k\rbrack} < 0},{{i_{p}\lbrack k\rbrack} < 0}} \\{- V_{dc}} & {{{\sigma\lbrack k\rbrack} < 0},{{i_{p}\lbrack k\rbrack} > 0}} \\0 & {{\sigma\lbrack k\rbrack} > 0}\end{matrix} } & (48)\end{matrix}$

Based on (48) a full-bridge converter according to an embodiment of thepresent invention can have four operation modes, which are presented inTable V. The presented operation modes can be determined according tothe sign of σ and peak resonant current i_(p) in each half-cycle. InFIG. 17, the resonant current path in four different operation modes ispresented, according to an embodiment of the present invention. Asdemonstrated in Table V and FIG. 17, the switching signals of thefull-bridge converter is as follows:S ₁=sign(i _(r)) S ₂=sign(i _(r))S ₃=sign(i _(r))·sign(σ[k]) S ₃=sign(i _(r))·sign(σ[k])  (49)

Similarly, control switching states for a half-bridge converter shown inFIG. 15B, according to an embodiment of the present invention, can be:

$\begin{matrix}{{u\lbrack {k + 1} \rbrack} = \{ \begin{matrix}V_{dc} & {{{\sigma\lbrack k\rbrack} < 0},{{i_{p}\lbrack k\rbrack} < 0}} \\0 & {{\sigma\lbrack k\rbrack} > 0}\end{matrix} } & (50)\end{matrix}$

TABLE VI SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN HALF-BRIDGECONTROLLER. Mode Type sign (i_(r)) sign (σ[k]) S₁ S₂ 1 energy injection1 1 1 0 2 free oscillation 0 X 0 1 3 free oscillation 1 0 0 0

Based on (50), a half-bridge converter will have three operation modes,which are presented in Table VI. These operation modes are determinedaccording to the sign of σ and peak resonant current i_(p) in eachhalf-cycle. The resonant current paths in four different operationmodes, according to an embodiment of the present invention, arepresented in FIG. 18. According to Table VI and FIG. 18, the switchingsignals of the full-bridge converter are:S ₁=sign(i _(r))·sign(σ[k]) S ₂=sign(i _(r))  (51)

Based on the control laws and corresponding switching signals derivedfor the full-bridge and half-bridge topologies, embodiments of thepresent invention can include SMCs designed for both topologies. Asimplified design for both technologies will be presented next.

A. Full-Bridge Converter

A self-tuning SMC for a full-bridge converter according to an embodimentof the present invention is shown in FIG. 18. The controller receivesfeedback from the resonant current of the LC tank as the input andgenerates the switching signals for the four switches of the full-bridgeinverter. The operation of the converter can be described in fouroperation modes, which are presented in Table V and FIG. 17. Theoperation modes 1 and 2 are energy injection modes in which energy isinjected to the LC tank, and the operation modes 3 and 4 are freeoscillation modes in which the LC tank continues its resonantoscillation. The transition of different modes of operation occurs ateach current zero-crossing point. Each mode starts at a resonant currentzero-crossing, and continues for a half cycle until the next resonantcurrent zero-crossing. This operation mode transition is determinedbased on the state of the circuit, as well as the user-defined referencevalues for the resonant current. The resonant current regulation can beachieved using a controller of the present invention by constantlyswitching between energy injection and free-oscillation modes.

The controller receives feedback from the resonant current of the LCtank as the input and generates the switching signals for the fourswitches of the full-bridge inverter. According to an embodiment of thepresent invention, the controller is composed of two differentialvoltage comparators, a peak detector, two D-type flip-flops, two ANDgates, and a NOT gate. The first differential comparator can be used todetect resonant current zero-crossing points, as well as its direction.This can be done by comparing the resonant current signal (measured by acurrent sensor) to the ground (zero voltage level). The peak detectorcan detect the peak of the resonant current in each half-cycle. TheD-type flip-flops save the state of the peak comparator for the nexthalf-cycle (sign(σ[k])). These two flip-flops can be used to considerboth positive and negative peaks of the resonant current. Similarly, theflip-flops are triggered using the output of the zero-cross comparator(sign(i_(r))). Since the direction of current changes at each currentzero-crossing, the flip-flop will be triggered at each currentzero-crossing point. Finally, AND and NOT gates can be used to generatethe appropriate switching signals for S₁, S₂, S₃ and S₄ according toTable V.

FIG. 19 shows a sliding mode controller for a full-bridge resonantinverter according to an embodiment of the present invention. Thefull-bridge sliding mode controller is designed based on the derivedswitching signals in equation (49). Based on (49), the controller takesthe resonance current signal (i_(r)) and reference current (i_(ref)) andgenerates the switching signals S₁, S₂, S₃, and S₄. The full-bridgesliding mode controller can be designed by using two differentialvoltage comparators, a peak detector, two D-type flip-flops, two ANDgates, and a NOT gate. The first differential comparator takes theresonant current measurement signal (i_(r)) as the input and generatessign(i_(r)) signal which represents the direction of the resonantcurrent, by comparing it to the zero level (ground). The NOT gate thentakes the sign(i_(r)) as an input used to output the sign(i_(r)) signal.The signal sign(σ[k]) can be generated based on equation (45). In orderto generate the sign(σ[k]) signal based on equation (45), the peakcurrent i_(p) and the reference current i_(ref) are compared. The peakdetector takes the i_(r) as input and outputs the peak current i_(p).The second differential comparator is used compare to the peak currenti_(p) and the reference current i_(ref) and generate sign(σ). Twoflip-flops are used to discretize sign(σ) by using the sign(i_(r)) andsign(i_(r)) as a clock source, in order to generate sign(σ[k]). Based on(49), S₁ and S₂ should be connected to the sign(i_(r)) and sign(i_(r))signals, respectively. Two AND gates can also be used to generate theswitching signals S₃ and S₄ by taking sign(i_(r)), sign(i_(r)) andsign(σ[k]) as inputs.

A self-tuning SMC for half-bridge converters, according to an embodimentof the present invention, is shown in FIG. 20. The half-bridge slidingmode controller is designed based on the derived switching signals inequation (51). Based on (51), the controller takes the resonance currentsignal (i_(r)) and reference current (i_(ref)) and generates theswitching signals S₁ and S₂. The full-bridge sliding mode controller canbe designed by using two differential voltage comparators, a peakdetector, a D-type flip-flop, an AND gate, and a NOT gate. The firstdifferential comparator takes the resonant current measurement signal(i_(r)) as the input and generates the sign(i_(r)) signal, whichrepresents the direction of the resonant current, by comparing it to thezero level (ground). The NOT gate then takes the sign(i_(r)) as an inputused to output the sign(i_(r)) signal. The signal sign(σ[k]) can begenerated based on equation (45). In order to generate the sign(σ[k])signal based on equation (45), the peak current i_(p) and the referencecurrent i_(ref) are compared. The peak detector takes the i_(r) as aninput and outputs the peak current i_(p). The second differentialcomparator is used to compare the peak current i_(p) and the referencecurrent i_(ref) and generates sign(σ). Two flip-flops are used todiscretize sign(σ) by using the sign(i_(r)) and sign(i_(r)) as a clocksource, in order to generate sign(σ[k]). Based on (51), S₂ should beconnected to the sign(i_(r)) signal and the AND gate is used to generateS₂ by taking sign(i_(r)), sign(i_(r)) and sign(σ[k]) as inputs.

The operation of the converter of FIG. 20 can be described in threemodes, which are presented in Table VI and FIG. 18. Operation mode 1 isenergy injection mode in which energy is injected to the LC tank.Operation modes 2 and 3 are free oscillation modes in which the LC tankcontinues its free oscillation. The transition of different modes ofoperation occurs at current zero-crossing points, which allows thecircuit to operate with greater efficiency. Each mode starts at aresonant current zero-crossing, and continues for a half cycle until thenext resonant current zero-crossing point. The operation mode transitionis determined based on the state of the circuit, as well as theuser-defined reference values for the resonant current. The resonantcurrent regulation can be achieved using a controller of the presentinvention by constantly switching between energy injection andfree-oscillation modes.

The controller takes a feed-back from the resonant current of the LCtank as the input and generates the switching signals for the twoswitches of the half-bridge inverter. It is composed of two differentialvoltage comparators, a half-cycle peak detector, a D-type flip-flop, anAND gate, and a NOT gate. The first differential comparator is used todetect resonant current zero-crossing points, as well as its direction.This is done by comparing the resonant current signal (measured by acurrent sensor) to the ground (zero voltage level). The peak detector isused to detect the peak of the resonant current of the LC tank in eachhalf-cycle. The D-type flip-flop is used to save the state of the peakcomparator for the next half-cycle (sign(σ[k])). This is achieved bytriggering the flip-flop, using the output of the zero-cross comparator(sign(i_(r))). Since the direction of current changes at each currentzero-crossing point, the flip-flop will be triggered at each currentzero-crossing point. Finally, AND and NOT gates are used to generate theappropriate switching signals for S₁ and S₂ according to Table VI.

Embodiments of the present invention include a variable frequencycontroller based on energy-injection free-oscillation techniques.Embodiments can be used for multi-level electric vehicle (EV) batterycharger applications based on IPT systems. Although variable controlmethods of the present invention can be applied to different convertertopologies, this application will present a controller that is designedfor three-phase full-bridge AC/DC/HFAC (high-frequency AC) converters. Acontroller according to an embodiment of the present invention canenable contactless charging of an EV based on a user-defined level andcan provide, for example, 11 charging levels (including standardcharging levels 1, 2 and 3). In addition, controllers of the presentinvention can self-tune switching operations to the resonance frequencyof the IPT system, and can benefit from zero-current switching (ZCS),which ensures maximum power transfer efficiency. Furthermore,controllers according to the present invention can be implemented witheither a digital or analog control circuit.

Embodiments of the present invention can effectively regulate resonantcurrent and output power in an IPT system using an energy-injection andfree-oscillation technique. Using energy injection and free-oscillation,resonant current can be controlled by regulating the energy transferrate that is injected to the primary LC tank. This can be accomplishedby constantly switching the operation mode of the converter between twofree-oscillation and energy-injection modes. The operation of aconverter according to an embodiment of the present invention can bedescribed in four modes as presented in Table VII and FIG. 25.

FIG. 24 is a diagram of a full-bridge AC/DC/HFAC converter with acontroller according to an embodiment of the present invention. Thecontroller can be designed based on an analog circuit, and can becomposed of D-type flip-flops, logic gates, a voltage comparator, andmultiport switches.

TABLE VII Switching states in different modes of operation. CurrentEnergy direction injection Mode Type (i > 0) enabled S₁ S₂ S₃ S₄ mode 1Energy injection 1 1 1 0 0 1 mode 2 Energy injection 0 1 0 1 1 0 mode 3Free oscillation 1 0 1 0 0 0 mode 4 Free oscillation 0 0 0 1 0 0

Flip-flops along with logic gates can be used to change the energyinjection rate to the LC tank, based on a user-defined level (Levels 1,2 and 3 charging power rates), thereby reducing the frequency of energyinjection half-cycles and increasing the number of free-oscillationcycles. As a result, using methods according to the present invention,the transferred power to the LC tank can be regulated. FIG. 26 showstypical waveforms of resonant current and output voltage with aninverter and controller according to an embodiment of the presentinvention. As it can be seen, each mode starts and ends at zero-crossingpoints, which leads to a soft-switching operation of the inverter.Therefore, converters according to the present invention can have higherefficiency compared to conventional converters. Furthermore, controllerswith analog design not only simplify implementation, but also enablehigher operating frequencies that conventional digital controllers(DSP/FPGA) may not be able to achieve.

According to embodiments of the present invention, the frequency ofenergy injection in both positive and negative half-cycles of theresonant current can be controlled. The energy injection frequency inpositive and negative half-cycles can be f_(r) (resonance frequency),f_(r)/2, f_(r)/4, f_(r)/8 and 0 (no energy injection). Thisfunctionality can allow for energy injection to the IPT system atdifferent levels. These different charging levels are presented in TableVIII. Different charging levels are achieved by using different energyinjection frequencies in positive and negative half-cycles. The voltageand the resonant current, which are shown in FIG. 26, correspond tolevel 10 charging level. It should be noted that although there are 14other combinations for energy injection frequencies for positive andnegative half-cycles, they can all be represented by one of the energyinjection levels which are given in Table VIII.

A theoretical evaluation of embodiments of the present invention willnow be presented, including analytical solutions for the resonantvoltage, resonant current and the output power.

The differential equation of a series compensated IPT system withprimary self-inductance of L, compensation capacitor C and an equivalentresistance R_(eq) can be expressed as:

$\begin{matrix}{{{{L\frac{di}{dt}} + {R_{eq}i} + {\frac{1}{C}{\int_{0}^{t}{i\; d\; t}}} + v_{c\; 0}} = V_{t}}\ } & (52)\end{matrix}$where i is the resonant current, v_(c) is the voltage of thecompensation capacitor, and V_(t) is the input voltage. Equation (52)can be rewritten as the following second order differential equation:

$\begin{matrix}{\frac{d^{2}i}{{dt}^{2}} = {{{\frac{R_{eq}}{L}\frac{di}{dt}} + {\frac{1}{LC}i}} = 0}} & (53)\end{matrix}$

At each current zero-crossing point, the initial conditions of thecircuit can be written as follows:

$\begin{matrix}{{i_{0} = 0},\mspace{14mu}{{L\frac{di}{dt}(0)} = {V_{t}\  - v_{c\; 0}}}} & (54)\end{matrix}$

The solution of (53) based on initial conditions in (54) is derived as:i=Ke ^(−t/τ)sin(ωt)  (55)wherein the natural damped frequency ω=√{square root over (ω₀ ²−α²)},resonant frequency ω₀=1√{square root over (LC)}, damping coefficientα=R_(eq)/2L, damping time constant τ=2L/R and the coefficient K isexpressed as:

$\begin{matrix}{K = \frac{V_{t}\  - v_{c\; 0}}{\omega\; L}} & (56)\end{matrix}$

TABLE VIII Different charging levels of variable frequency energyinjection control. Frequency of energy injection Charging Level Positivehalf-cycles Negative half-cycles 1 f_(r) f_(r) 2 f_(r) f_(r)/2 3 f_(r)f_(r)/4 4 f_(r) f_(r)/8 5 f_(r)/2 f_(r)/2 6 f_(r)/2 f_(r)/4 7 f_(r)/2f_(r)/8 8 f_(r)/4 f_(r)/4 9 f_(r)/4 f_(r)/8 10 f_(r)/8 f_(r)/8 11f_(r)/8 0

Equation (55) shows that the peak current decreases exponentially withtime constant τ and (56) shows that the value of K changes in each halfcycle depending on the input voltage and initial voltage of thecompensation capacitor. It should be noted that in the free oscillationmodes, the input voltage is zero (V_(t)=0). Also the compensationcapacitor voltage can be expressed as:

$\begin{matrix}{{v_{c}(t)} = {v_{c\; 0} + {\frac{K\;\tau}{C( {1 + {\tau^{2}\omega^{2}}} )}( {{\tau\;\omega} - {e^{{- t}/\tau}\lbrack {{\sin( {\omega\; t} )} + {\tau\; w\;{\cos( {\omega\; t} )}}} \rbrack}} )}}} & (57)\end{matrix}$

Using (56), the resonant current in a time period composed of bothenergy injection and free oscillation modes can be expressed as follows:

$\begin{matrix}{{i(t)} = \{ \begin{matrix}{K_{i}e^{{- t}/\tau}{\sin( {\omega\; t} )}} & {0 < t < \frac{\pi}{\omega}} \\{K_{f}e^{{- t}/\tau}{\sin( {\omega\; t} )}} & {\frac{\pi}{\omega} < t < \frac{2\; n\;\pi}{\omega}}\end{matrix} } & (58)\end{matrix}$where n denotes the total number of half-cycles, which is composed ofone energy injection half-cycle and 2n−1 free oscillation half-cycles,and K_(i) and K_(f) are coefficients of (56) in the first energyinjection and free oscillation half-cycles respectively, which can becalculated using (56) as follows:

$\begin{matrix}{{K_{i} = {\frac{1}{\omega\; L}\lbrack {V_{t} - v_{c\; 0}} \rbrack}}{K_{f} = {{\frac{1}{\omega\; L}\lbrack {v_{c}( \frac{\pi}{\omega} )} \rbrack} = {\frac{1}{\omega\; L}\lbrack {{v_{c}(0)} + {\frac{K_{i}\tau^{2}\omega}{C( {1 + {\tau^{2}\omega^{2}}} )}( {1 + e^{{- \pi}/{\tau\omega}}} )}} \rbrack}}}} & (59)\end{matrix}$

In order to calculate the initial condition for the resonant voltage ateach current zero-crossing in a steady-state condition, a full controlcycle consisting of 2n half-cycles of the resonant current, whichincludes one energy injection half-cycle (FIG. 26), is considered. Theresonant voltage at the end of the energy injection half-cycle (t=π/ω)can be calculated using (57) as follows:v _(c1) =V _(t)+β(V _(t) −v _(c0))  (60)where β is defined as:

$\begin{matrix}{\beta = e^{\frac{- \pi}{\tau\omega}}} & (61)\end{matrix}$

At the end of free-oscillation half-cycles (half-cycles from 2 to 2n),the resonant voltage can be calculated based on (57) as follows:v _(ck) =v _(c1)β^(k-1)(−1)^(k-1)  (62)

Using (60), equation (62) can be rewritten as follows:v _(ck) =V _(t)(1+β)β^(k-1)(−1)^(k-1) +v _(c0)β^(k)  (63)

By assuming that the system has reached a steady-state condition, it canbe concluded that the resonant voltage at the beginning of each controlcycle (v_(c0) at k=0) should be equal to its value at the end of thecontrol cycle (v_(ck) at k=2n). Therefore, using (63) the followingequations can be derived:

$\begin{matrix}{v_{c\; 0} = {{{- {V_{t}( {1 + \beta} )}}\beta^{{2\; n} - 1}} + {v_{c\; 0}\beta^{2\; n}}}} & (64) \\{v_{c\; 0} = {{- \frac{( {1 + \beta} )}{1 - \beta^{2\; n}}}\beta^{{2\; n} - 1}V_{t}}} & (65)\end{matrix}$

Equation (65) is the initial condition for the resonant voltage in thesteady-state condition and can be used in (56), (57), and (59) tocalculate the resonant current and the resonant voltage at any time.

The maximum output power of a converter according to the presentinvention can be achieved when the controller is set to level 1. In thiscase, all of the half-cycles of the resonant current are in an energyinjection mode. Using the same method for calculation of the initialcondition for the resonant voltage in steady-state conditions, theinitial condition for the resonant voltage can be calculated as follows:

$\begin{matrix}{v_{c\; 0} = {{- \frac{1 + \beta}{1 - \beta}}V_{t}}} & (66)\end{matrix}$

Using (59), the resonant current i for any half-cycle can be written asfollows:

$\begin{matrix}{i = {\frac{2\; V_{t}}{\omega\;{L( {1 - \beta} )}}e^{{- t}/\tau}{\sin( {\omega\; t} )}}} & (67)\end{matrix}$

The output power can be calculated using (67) as follows:

$\begin{matrix}{P = \frac{\int_{0}^{\pi/\omega}{V_{t}\frac{2\; V_{t}}{\omega\;{L( {1 - \beta} )}}e^{{- t}/\tau}{\sin( {\omega\; t} )}{dt}}}{\pi/\omega}} & (68) \\{P = \frac{2\; V_{t}^{2}\tau^{2}{\omega( {1 + e^{{- \pi}/{\tau\omega}}} )}}{\pi\;{L( {1 - \beta} )}( {1 + {\tau^{2}\omega^{2}}} )}} & (69)\end{matrix}$

Using (69), the output power can be calculated based on the inputvoltage and the circuit parameters.

The subject invention includes, but is not limited to, the followingexemplified embodiments.

Embodiment 1

A three-phase ac-ac matrix converter for inductive power transfer (IPT)systems comprising:

-   -   a first line, a second line, a third line, and a fourth line,        all of which are connected in parallel;        -   a first phase input connected to the first line, a second            phase input connected to the second line, and a third phase            input connected to the third line;    -   a first switch and a second switch connected in series on the        first line and on opposite sides of a first phase input        connection;    -   a third switch and a fourth switch connected in series on the        second line and on opposite sides of a second phase input        connection;    -   a fifth switch and a sixth switch connected in series on the        third line and on opposite sides of a third phase input        connection;    -   a seventh switch on the fourth line.

Embodiment 2

The three-phase ac-ac matrix converter of Embodiment 1, wherein thefirst switch, the second switch, the third switch, the fourth switch,the fifth switch, and the sixth switch are all reverse blockingswitches, each including an IGBT or a MOSFET in series with a diode.

Embodiment 3

The three-phase ac-ac matrix converter of Embodiment 1, wherein thefirst switch, the second switch, the third switch, the fourth switch,the fifth switch, and the sixth switch are switches with built-inreverse blocking functionality.

Embodiment 4

The direct three-phase ac-ac matrix converter of any of Embodiments 1 to3, wherein a diode is connected in parallel with the seventh switch andon the fourth line.

Embodiment 101

A method for direct three-phase ac-ac matrix conversion for inductivepower transfer (IPT) comprising:

-   -   providing a three-phase ac-ac matrix converter including:        -   a first line, a second line, a third line, and a fourth            line, all of which are connected in parallel;        -   a first phase input connected to the first line and having a            first phase input voltage V_(a), a second phase input            connected to the second line and having a second phase input            voltage V_(b), and a third phase input connected to the            third line and having a third phase input voltage V_(c);        -   a first switch S_(A1) and a second switch S_(A2) connected            in series on the first line and on opposite sides of a first            phase input connection;        -   a third switch S_(B1) and a fourth switch S_(B2) connected            in series on the second line and on opposite sides of a            second phase input connection;        -   a fifth switch S_(C1) and a sixth switch S_(C2) connected in            series on the third line and on opposite sides of a third            phase input connection; and        -   a seventh switch S_(F) on the fourth line;    -   changing how current flows through the three-phase ac-ac matrix        converter based on one or more control modes.

Embodiment 102

The method of Embodiment 101, wherein the first switch, the secondswitch, the third switch, the fourth switch, the fifth switch, and thesixth switch are all reverse blocking switches, each including an IGBTor a MOSFET in series with a diode.

Embodiment 103

The method of Embodiment 101, wherein the first switch, the secondswitch, the third switch, the fourth switch, the fifth switch, and thesixth switch are switches with built-in reverse blocking functionality.

Embodiment 104

The method of any of Embodiments 101 to 103, wherein the control modesinclude a current regulation control mode, a voltage regulation controlmode, and a power regulation control mode.

Embodiment 105

The method of any of Embodiments 101 to 103, further comprisingproviding a seventh diode D_(F) that is in parallel with the seventhswitch SF on the fourth line in the three-phase ac-ac matrix converter.

Embodiment 106

The method of any of Embodiments 101 to 105, further comprising:

-   -   providing a reference current i_(ref);    -   providing a reference voltage v_(ref);    -   providing a reference power P_(ref);    -   measuring a peak output resonance current i_(p); and    -   measuring output power P_(out).

Embodiment 107

The method of any of Embodiments 101 to 106, wherein the three-phaseac-ac matrix converter operates in a current regulation control modeaccording to rules in the following table:

SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN CURRENT REGULATIONCONTROL MODE. Conducting Mode Resonant Current Input Voltages Switches 1i_(p) < 0, |i_(p)| < i_(ref) V_(b) < V_(c) < V_(a) S_(A1), S_(B2) 2i_(p) < 0, |i_(p)| < i_(ref) V_(c) < V_(b) < V_(a) S_(A1), S_(C2) 3i_(p) < 0, |i_(p)| < i_(ref) V_(a) < V_(c) < V_(b) S_(B1), S_(A2) 4i_(p) < 0, |i_(p)| < i_(ref) V_(c) < V_(a) < V_(b) S_(B1), S_(C2) 5i_(p) < 0, |i_(p)| < i_(ref) V_(b) < V_(a) < V_(c) S_(C1), S_(B2) 6i_(p) < 0, |i_(p)| < i_(ref) V_(a) < V_(b) < V_(c) S_(C1), S_(A2) 7i_(p) < 0, |i_(p)| > i_(ref) — D_(F) 8 i_(p) >0 — S_(F)

Embodiment 108

The method of any of Embodiments 101 to 107, wherein the three-phaseac-ac matrix converter operates in a voltage regulation control modeaccording to the rules in following table:

SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN VOLTAGE REGULATIONCONTROL MODE. Conducting Mode Resonant Voltage & Current Input VoltagesSwitches 1 v_(p) < 0, |v_(p)| < v_(ref) V_(b) < V_(c) < V_(a) S_(A1),S_(B2) 2 v_(p) < 0, |v_(p)| < v_(ref) V_(c) < V_(b) < V_(a) S_(A1),S_(C2) 3 v_(p) < 0, |v_(p)| < v_(ref) V_(a) < V_(c) < V_(b) S_(B1),S_(A2) 4 v_(p) < 0, |v_(p)| < v_(ref) V_(c) < V_(a) < V_(b) S_(B1),S_(C2) 5 v_(p) < 0, |v_(p)| < v_(ref) V_(b) < V_(a) < V_(c) S_(C1),S_(B2) 6 v_(p) < 0, |v_(p)| < v_(ref) V_(a) < V_(b) < V_(c) S_(C1),S_(A2) 7 v_(p) < 0, |v_(p)| > v_(ref) — D_(F) 8 i_(p) >0 — S_(F)

Embodiment 109

The method of any of Embodiments 101 to 108, wherein the three-phaseac-ac matrix converter operates in a power regulation control modeaccording to rules in the following table:

SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN POWER REGULATIONCONTROL MODE. Output Power & Resonant Conducting Mode Current InputVoltages Switches 1 P_(out) < P_(ref), i_(p) < 0 V_(b) < V_(C) < V_(a)S_(A1), S_(B2) 2 P_(out) < P_(ref), i_(p) < 0 V_(c) < V_(b) < V_(a)S_(A1), S_(C2) 3 P_(out) < P_(ref), i_(p) < 0 V_(a) < V_(c) < V_(b)S_(B1), S_(A2) 4 P_(out) < P_(ref), i_(p) < 0 V_(c) < V_(a) < V_(b)S_(B1), S_(C2) 5 P_(out) < P_(ref), i_(p) < 0 V_(b) < V_(a) < V_(c)S_(C1), S_(B2) 6 P_(out) < P_(ref), i_(p) < 0 V_(a) < V_(b) < V_(c)S_(C1), S_(A2) 7 P_(out) > P_(ref), i_(p) < 0 — D_(F) 8 i_(p) >0 — S_(F)

Embodiment 110

The method of any of Embodiments 101 to 109, wherein the control modesare based on zero current switching operations or resonant zero crossingpoints.

Embodiment 201

A half-bridge sliding mode controller comprising:

-   -   a first comparator suitable for detecting resonant current        zero-crossing points and current direction, wherein the first        comparator compares a resonant current signal to a ground;    -   a half-cycle peak detector that detects a peak resonant current        in each half cycle and having the resonant current signal as an        input;    -   a second comparator having a reference current and an output of        the half-cycle peak detector as inputs;    -   a D-type flip-flop that saves a state of the second comparator        for the next half-cycle using an output of the first comparator        S_(sgn) and an output of the second comparator as inputs;    -   an AND gate having the output of the first comparator S_(sgn)        and an output of the D-type flop S_(inj) as inputs, and        outputting a first switching signal S₁; and    -   a NOT gate having the output of the first comparator S_(sgn) as        an input and outputting a second switching signal S₂.

Embodiment 202

A method for operating a half-bridge resonant converter comprising:

-   -   providing the half-bridge sliding mode controller of Embodiment        201, wherein the half bridge sliding mode controller operates        according to the following modes:

Mode Type S_(agn) S_(inj) S₁ S₂ 1 energy injection 1 1 1 0 2 freeoscillation 0 X 0 1 3 free oscillation 1 0 0 0

Embodiment 203

The method of Embodiment 202, wherein the transition to different modesoccurs at zero-crossing points and allows for soft switching operations.

Embodiment 301

A full-bridge sliding mode controller comprising:

-   -   a first comparator suitable for detecting resonant current        zero-crossing points and current direction, wherein the first        comparator compares a resonant current signal to a ground, and        wherein the first compactor outputs a first switching signal S₁;    -   a peak detector that detects a peak resonant current and having        the resonant current signal as an input;    -   a second comparator having a reference current and an output of        the peak detector as inputs;    -   a first D-type flip-flop having an output of the second        comparator as an input;    -   a second D-type flip-flop having an output of the first        comparator and the output of the second comparator as inputs;    -   a NOT gate having the output of the first comparator as an input        and outputting a second switching signal S₂;    -   a first AND gate having outputs of the first D-flip flop as        inputs and outputting a third switching signal S₃; and    -   a second AND gate having the output of the first comparator and        an output of the second D-type flop as inputs, and outputting a        fourth switching signal S₄.

Embodiment 302

A method for operating a full-bridge resonant converter comprising:

-   -   providing the full-bridge sliding mode controller of Embodiment        301, wherein the full-bridge sliding mode controller operates        according to the following modes:

Mode Type S_(sgn) S_(inj) S₁ S₂ S₃ S₄ 1 energy injection 1 1 1 0 0 1 2energy injection 0 1 0 1 1 0 3 free oscillation 1 0 1 0 0 0 4 freeoscillation 0 0 0 1 0 0.

Embodiment 303

The method of Embodiment 202, wherein the transition to different modesoccurs at zero-crossing points and allows for soft switching operations.

Embodiment 401

A method for operating a full-bridge converter comprising:

-   -   providing a full-bridge converter having a topology of FIG. 15A,        or an equivalent topology; and    -   operating the full-bridge converter according to the following        switching states,

Mode Type sign(i_(r)) sign(σ[k]) S₁ S₂ S₃ S₄ 1 energy injection 1 1 1 00 1 2 energy injection 0 1 0 1 1 0 3 free oscillation 1 0 1 0 0 0 4 freeoscillation 0 0 0 1 0 0.

Embodiment 402

A method for operating a half-bridge converter comprising:

-   -   providing a half-bridge converter having a topology of FIG. 15B,        or an equivalent topology; and    -   operating the half-bridge converter according to the following        switching states,

Mode Type sign (i_(r)) sign (σ[k]) S₁ S₂ 1 energy injection 1 1 1 0 2free oscillation 0 X 0 1 3 free oscillation 1 0 0 0.

Embodiment 501

A sliding mode controller for a full-bridge resonant inverter having atopology of FIG. 19 (the lower portion), or an equivalent topology.

Embodiment 502

A sliding mode controller for a half-bridge resonant inverter having atopology of FIG. 20 (the lower portion), or an equivalent topology.

Embodiment 601

A controller for inductive power transfer having a topology of FIG. 24(the lower portion), or an equivalent topology.

Embodiment 701

A controller and converter combination for inductive power transferhaving a topology of FIG. 24 (the entire figure), or an equivalenttopology.

Embodiment 702

The controller and converter combination for inductive power transfer ofEmbodiment 701, wherein the controller and converter combination canoperate according to one or more of the following charging levels:

Frequency of energy injection Charging Level Positive half-cyclesNegative half-cycles 1 f_(r) f_(r) 2 f_(r) f_(r)/2 3 f_(r) f_(r)/4 4f_(r) f_(r)/8 5 f_(r)/2 f_(r)/2 6 f_(r)/2 f_(r)/4 7 f_(r)/2 f_(r)/8 8f_(r)/4 f_(r)/4 9 f_(r)/4 f_(r)/8 10 f_(r)/8 f_(r)/8 11 f_(r)/8 0,wherein fr is resonance frequency of the converter.

A greater understanding of the present invention and of its manyadvantages may be had from the following examples, given by way ofillustration. The following examples are illustrative of some of themethods, applications, embodiments and variants of the presentinvention. They are, of course, not to be considered as limiting theinvention. Numerous changes and modifications can be made with respectto the invention.

Example 1—Simulation of Converter Topology and Control Modes Accordingto an Embodiment of the Present Invention

A three-phase converter according to an embodiment of the presentinvention was simulated using MATLAB/SIMULINK. The IPT model that wassimulated is shown in FIG. 5. This model was composed of a three-phasepower supply with an output LC filter, the primary three-phase ac-acconverter, the primary and secondary magnetic structures with theircorresponding compensation capacitors and the secondary load, which is abattery charger of an electric vehicle. The controller of the primaryconverter and its components are also shown in FIG. 5. The measurementsinclude the three-phase input voltage and the output resonant current ofthe LC tank. The controller is triggered in each resonant currentzero-crossing and, based on the voltage and current measurements, theswitching state of the of the converter was determined. The switchingsignals of the converter were not changed until the next currentzero-crossing.

The self-inductances of the primary and secondary were each 168 μH, andeach had a 1 μF compensation capacitor and the operating frequency ofthe converter, which is equal to the resonance frequency of the LC tank,was 12.28 kHz. The line-to-line voltage of the three-phase supply was208 V. The current regulation control mode was enabled with a 282.8 A(200 Arms) reference current. The simulation results including thethree-phase input voltages and their corresponding modes of operation,the output resonant current and corresponding switching signals ofS_(A1), S_(B1), S_(C2), S_(F), are shown in FIG. 7. Also, the frequencyspectrum of the output resonant current is shown in FIG. 8. As can beseen in FIGS. 7 and 8, the current is fully regulated around thereference current and its THD was 9.22%. The active and reactive powercalculations show that the total output power is 18.4 kW and thefundamental reactive power is zero (Q₁=0) and, therefore, thedisplacement power factor is unity (DPF=1).

However, due to higher order harmonics in the three-phase input voltagesand currents, the true power factor is 0.76. Using the specificationsgiven in Table IV for the switches of the converter, the efficiency ofthe converter was calculated through the simulation to be 96.2%, basedon equations (21)-(25).

Example 2—Experimental Analysis of Converter Topology and Control ModesAccording to an Embodiment of the Present Invention

An experimental proof of concept study was performed on an IPT systemaccording to an embodiment of the present invention, as shown in FIG. 9.This system was composed of two circular magnetic structures with 700 mmdiameters and a 200 mm air gap. The circular power pads were composed ofcoils, ferrite bars, and aluminum shields. A three-phase matrixconverter according to an embodiment of the present invention was usedas the primary converter with a series-parallel topology, as shown inFIG. 5. The self-inductance of each circular pad was 168 μH, and 1 μFcompensation capacitors were used in both primary and secondarycircuits. The line voltage of the three-phase power supply was 40 V. Inthis experimental study, a series combination of a MOSFET (IRF3205) witha diode (DSEP 30-12A) was used to make reverse the blocking switches.However, switches with built-in (or intrinsic) reverse blockingcapability are available in the market (e.g., IXRH-40N120) or can becustom fabricated, either of which could be used instead. The switchS_(F) was also an IRF3205 MOSFET, and its body diode was used as thediode D_(F). A STM32F4-discovery board with an ARM Cortex-M4 168 MHz DSPwas used as the main controller. The resonant current regulation andoutput power regulation control strategies were studied on the prototypeIPT system. This analysis will be described in the following paragraphs.

Resonant current regulation controls with a 14.1 A (10 Arms) referencecurrent was used to regulate the resonance current. FIG. 10 shows theoutput resonant current and corresponding switching signals of S_(A1),S_(B1) and S_(F) during the transition of the most positive phase involtage from phase A to phase B. The operating frequency of theconverter was 12.25 kHz, which has a small discrepancy compared to thetheoretical resonance frequency (12.28 kHz). The waveforms of the inputvoltage (V_(a)), input current (i_(a)), input power (P_(out)) for phaseA and output resonant current are shown in FIG. 11. As can be seen, theresonant current is fully regulated around the reference current.However, the input voltage has high frequency harmonics which willreduce the true power factor of the converter as a result. It will alsoreduce the power transfer efficiency of the converter. The frequencyspectrum of the output resonant current was measured experimentally,which is shown in FIG. 12. Calculations show that the THD of the outputresonant current was 14.3%. The total output power was 267 W (89 W fromeach phase). The input power factor measurements show that the truepower factor was 0.67. However, the fundamental reactive power was zeroand, therefore, the displacement power factor was unity. Also, themeasured loss of the converter was 31.5 W and, consequently, theefficiency of the converter was 89.4% compared to a 92.7% theoreticalefficiency calculated using (21)-(25).

The output power control mode with a 130 W reference power was used toregulate the output power. The output power and the output resonantcurrent are shown in FIG. 13. Similar to the current regulation control,the operating frequency of the converter was 12.25 kHz. While theaverage output power (P_(out)) was maintained at 136.4 W, the peakinstantaneous output power was 510 W and the RMS resonant current was7.81 A. The true power factor and displacement power factor were 0.59and 1, respectively. Measurements show that the total converter loss was25.1 W and, as a result, the efficiency of the converter was 84.46%compared to a 87.9% theoretical efficiency calculated using (21)-(25).

The dominant factors in converters are the speed of the controller (DSPboard) and the response delay time of the resonant current measurement.In IPT applications, high-frequency operation of the converter (10-85kHz) is essential to maximize the power transfer efficiency. On theother hand, in a converter according to an embodiment of the presentinvention, current and voltage measurements using analog to digitalconversion (ADC) with high sampling rates are required. Also, theimplemented control strategy on the digital signal processor (DSP),which consists of floating-point operations and comparisons, etc, alongwith ADC conversions, takes tens of clock cycles of the DSP to execute.As a result, a DSP with a high clock speed is essential. The maximumfrequency that can be practically achieved using the DSP board(STM32F4-discovery ARM Cortex-M4 168 MHz DSP) was about 40 kHz. However,controllers according to the present invention have the potential to beimplemented based on an analog circuit, which can significantly enhancethe controller speed and resolve the DSP issues.

A Hall-effect current transducer “LA 55-P” was used for the resonantcurrent measurement, which has a response delay less than 1 μs.Considering the fact that at least 20 samples in a full-cycle of theresonant current are required for a proper performance of the converter(without losing the zero-crossing points), the maximum frequency thatcan practically be achieved in this embodiment was about 50 kHz, basedon the response time delay of the current measurement.

In summary, the simulation analysis and experimental implementationsshow that converter topologies and control methods according to thepresent invention can fully regulate output current and output poweraround user-defined reference values. These factors make them wellsuited for dynamic IPT applications in which the system has inherentvariations.

Example 3—Experimental Analysis of a Sliding Mode Controller for aFull-Bridge Converter According to an Embodiment of the PresentInvention

An SMC circuit according to an embodiment of the present invention wassimulated in a proof of concept experiment. Specifically, an SMC circuitfor a full-bridge converter as shown in FIG. 19 was simulated usingMATLAB/Simulink. The simulation model was composed of a three-phasepower supply, transmitter and receiver pads with their correspondingcompensation capacitors, a full bridge AC/DC/AC converter that wascontrolled by an SMC embodiment and connected to the transmitter coil,and a 14 kW battery charger for an electric vehicle at the secondary.The self-inductances of the primary and secondary are each 172 μH,wherein each have a 0.12 μF compensation capacitor. As a result, theoperating resonance frequency of the LC tank was 35 kHz. The three-phasepower supply had a line-to-line voltage of 208 V with 60 Hz powerfrequency.

The simulations were carried out by setting the reference current of theSMC (i_(ref)) to 60 A and 100 A. FIGS. 21A and 21B show the resonantcurrent and the corresponding switching signals for both simulations. Asdemonstrated by FIGS. 21A and 21B, the switches 1 and 2 switchconstantly while switches 3 and 4 have variable switching signals. Theseswitching signals are adjusted by the SMC to control energy injection tothe IPT system and regulate the resonant current.

Example 4—Experimental Analysis of an SMC Design According to anEmbodiment of the Present Invention

A proof of concept experiment was conducted to verify the performance ofan SMC design according to an embodiment of the present invention. Acontroller for full-bridge converter topology was built based on thecircuit of FIG. 19, and experimental tests on an IPT system wereconducted. An image of the IPT system can be seen in FIG. 22, and wascomprised of two circular power pads as transmitter and receiverstructures, compensation capacitors, a full bridge AC/DC/AC converter,along with the an SMC circuit according to an embodiment of the presentinvention. The self-inductance of the circular pads was each 172 μH, andeach had a 0.12 μF compensation capacitor. As a result, the operatingresonance frequency of the LC tank was 35 kHz. A variable three-phasepower supply was used as the AC mains. The experimental tests werecarried out in two scenarios in order to demonstrate the performance ofthe (a) VLL=10V and iref=3:6 A, and (b) V_(LL)=20V and i_(ref)=10 A,where V_(LL) is the line-to-line voltage of the three-phase inputvoltage. In FIG. 23, the resonant current and energy injection switchingsignals (S₃ and S₄) of the full-bridge converter are shown. Theseresults show that an SMC circuit according to an embodiment of thepresent invention is capable of regulating the resonance current aroundthe reference current at different input voltage levels withsoft-switching operations.

Example 5—Simulation of an IPT System According to an Embodiment of thePresent Invention

A simulation of a controller according to the present invention wasconducted at different charging levels using MATLAB/Simulink.Furthermore, a controller according to an embodiment of the presentinvention, along with an AC/DC/AC converter, was implementedexperimentally on a proof of concept IPT system to verify performance atdifferent controller charging levels. The experimental test resultsconcurred with simulated experiments, supporting the assertion thatembodiments of the present invention can effectively enable self-tuningcapability and soft-switching operations at different charging levelsfor an IPT based contactless charging system.

MATLAB/Simulink was used for simulations at different charging levels.Furthermore, a controller according to an embodiment of the presentinvention was built and tested experimentally to prove the concept atdifferent charging levels.

A converter and analog control circuit, which is presented in FIG. 24,was simulated using MATLAB/Simulink. The simulation model was composedof a three-phase power supply, a rectifier, transmitter and receivercoils with corresponding compensation capacitors, an AC/DC/AC converterthat is controlled by the controller and connected to the transmittercoil, and a battery charger that simulated an electric vehicle at thesecondary. The self-inductances of the primary and secondary were each172 μH, wherein each had a 0.12 μF compensation capacitor. Therefore,the operating frequency of the converter, which is equal to theresonance frequency of the LC tank, was 35 kHz. The three-phase powersupply had a line-to-line voltage of 208 V with 60 Hz power frequency.

The simulations were carried out in four charging levels (levels 1, 5, 8and 10 according Table VIII), and the results are presented in Table IX.In addition, resonant current and voltage and corresponding switchingsignals are shown in FIG. 27. As can be seen, using a controlleraccording to the present invention, different charging levels can beachieved with low current harmonic distortions (THD).

TABLE IX The simulation results at charging, levels 1, 5, 8 and 10. RMSResonant THD of Charging Level Current (A) Current (%) Output Power (kW)Level 1 237.10 0.7 52.74 Level 5 120.60 1.7 13.7 Level 8 63.63 2.9 3.52Level 10 33.31 6.7 0.89

Example 6—Experimental Analysis of an IPT System According to anEmbodiment of the Present Invention

A multi-level controller according to an embodiment of the presentinvention was implemented experimentally and tested in a proof ofconcept IPT system as shown in FIG. 28. The IPT system consisted of twocircular transmitter and receiver power pads, compensation capacitors, athree-phase AC/DC/AC converter as the primary converter connected theproposed controller, and a 100 W load at the secondary. Theself-inductance of the power pads was 172 μH, and each pad had a 0.12 μFcompensation capacitor. Thereby, the operating frequency of theconverter, which was equal to the resonance frequency of the LC tank,was 35 kHz. The three-phase input was connected to a three-phase sourcewith a reduced line-to-line voltage of 25 V, with a 60 Hz frequency.

TABLE X Experimental test results on the case study IPT system using theproposed controller at different charging levels. Frequency of energyinjection Positive Negative Resonant Output Charging Level half-cycleshalf-cycles current (A) power (W) 1 f_(r) f_(r) 8.00 165.76 2 f_(r)f_(r)/2 5.81 87.42 3 f_(r) f_(r)/4 4.74 58.19 4 f_(r) f_(r)/8 4.19 45.475 f_(r)/2 f_(r)/2 3.64 34.32 6 f_(r)/2 f_(r)/4 2.59 17.37 7 f_(r)/2f_(r)/8 2.12 11.64 8 f_(r)/4 f_(r)/4 1.70 7.48 9 f_(r)/4 f_(r)/8 1.294.31 10 f_(r)/8 f_(r)/8 0.82 1.74 11 f_(r)/8 0 0.38 0.37

The controller was tested at 11 charging levels according to Table VIIIand the results are presented in Table X. The resonant current and theswitching signals are shown in FIG. 29. FIG. 29 demonstrates that, dueto the self-tuning capability of the converter, the switching operationsare all synced with the resonant current (at 35 kHz resonancefrequency). Furthermore, it can be seen that the switching operationsall happen at current zero-crossing points, which verifies thesoft-switching functionality of the converter (ZCS). Therefore,controllers according to an embodiment of the present invention caneffectively enable self-tuning capability and soft-switching operationat 11 charging levels.

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What is claimed is:
 1. A three-phase ac-ac matrix converter forinductive power transfer (IPT) systems comprising: a first line, asecond line, a third line, and a fourth line, all of which are connectedin parallel; a first phase input connected to the first line, a secondphase input connected to the second line, and a third phase inputconnected to the third line; a first switch and a second switchconnected in series on the first line and on opposite sides of a firstphase input connection; a third switch and a fourth switch connected inseries on the second line and on opposite sides of a second phase inputconnection; a fifth switch and a sixth switch connected in series on thethird line and on opposite sides of a third phase input connection; aseventh switch on the fourth line; and a diode connected in parallelwith the seventh switch and on the fourth line, the seventh switch beingdirectly connected to the first switch, the second switch, the thirdswitch, the fourth switch, the fifth switch, and the sixth switch, thefirst switch, the second switch, the third switch, the fourth switch,the fifth switch, and the sixth switch all being unidirectional, reverseblocking switches, each including an IGBT or a MOSFET in series with arespective diode, and the seventh switch being a bidirectional switch,and the three-phase ac-ac matrix converter being configured to operatein a current regulation control mode according to rules in the followingtable: SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN CURRENTREGULATION CONTROL MODE. Conducting Mode Resonant Current Input VoltagesSwitches 1 ip < 0, |ip| < i_(ref) V_(b) < V_(c) < V_(a) S_(A1), S_(B2) 2ip < 0, |ip| < i_(ref) V_(c) < V_(b) < V_(a) S_(A1), S_(C2) 3 ip < 0,|ip| < i_(ref) V_(a) < V_(c) < V_(b) S_(B1), S_(A2) 4 ip < 0, |ip| <i_(ref) V_(c) < V_(a) < V_(b) S_(B1), S_(C2) 5 ip < 0, |ip| < i_(ref)V_(b) < V_(a) < V_(c) S_(C1), S_(B2) 6 ip < 0, |ip| < i_(ref) V_(a) <V_(b) < V_(c) S_(C1), S_(A2) 7 ip < 0, |ip| > i_(ref) — D_(F) 8 ip >0 —S_(F,)

where: S_(A1) is the first switch; S_(A2) is the second switch; S_(B1)is the third switch; S_(B2) is the fourth switch; S_(C1) is the fifthswitch; S_(C2) is the sixth switch; S_(F) is the seventh switch; V_(a)is a first phase input voltage of the first phase input; V_(b) is asecond phase input voltage of the second phase input; V_(c) is a thirdphase input voltage of the third phase input; D_(F) is the diodeconnected in parallel with the seventh switch; i_(ref) is a referencecurrent provided to the three-phase ac-ac matrix converter; and i_(p) isa peak output resonance current of the three-phase ac-ac matrixconverter.
 2. A three-phase ac-ac matrix converter for inductive powertransfer (IPT) systems comprising: a first line, a second line, a thirdline, and a fourth line, all of which are connected in parallel; a firstphase input connected to the first line, a second phase input connectedto the second line, and a third phase input connected to the third line;a first switch and a second switch connected in series on the first lineand on opposite sides of a first phase input connection; a third switchand a fourth switch connected in series on the second line and onopposite sides of a second phase input connection; a fifth switch and asixth switch connected in series on the third line and on opposite sidesof a third phase input connection; a seventh switch on the fourth line;and a diode connected in parallel with the seventh switch and on thefourth line, the seventh switch being directly connected to the firstswitch, the second switch, the third switch, the fourth switch, thefifth switch, and the sixth switch, the first switch, the second switch,the third switch, the fourth switch, the fifth switch, and the sixthswitch all being unidirectional reverse blocking switches, eachincluding an IGBT or a MOSFET in series with a respective diode, and theseventh switch being a bidirectional switch, and the three-phase ac-acmatrix converter being configured to operate in a voltage regulationcontrol mode according to the rules in following table: SWITCHING STATESIN DIFFERENT MODES OF OPERATION IN VOLTAGE REGULATION CONTROL MODE.Resonant Voltage & Conducting Mode Current Input Voltages Switches 1 vp< 0, |vp| < v_(ref) V_(b) < V_(c) < V_(a) S_(A1), S_(B2) 2 vp < 0, |vp|< v_(ref) V_(c) < V_(b) < V_(a) S_(A1), S_(C2) 3 vp < 0, |vp| < v_(ref)V_(a) < V_(c) < V_(b) S_(B1), S_(A2) 4 vp < 0, |vp| < v_(ref) V_(c) <V_(a) < V_(b) S_(B1), S_(C2) 5 vp < 0, |vp| < v_(ref) V_(b) < V_(a) <V_(c) S_(C1), S_(B2) 6 vp < 0, |vp| < v_(ref) V_(a) < V_(b) < V_(c)S_(C1), S_(A2) 7 vp < 0, |vp| > v_(ref) — D_(F) 8 ip >0 — S_(F,)

where: S_(A1) is the first switch; S_(A2) is the second switch; S_(B1)is the third switch; S_(B2) is the fourth switch; S_(C1) is the fifthswitch; S_(C2) is the sixth switch; S_(F) is the seventh switch; V_(a)is a first phase input voltage of the first phase input; V_(b) is asecond phase input voltage of the second phase input; V_(c) is a thirdphase input voltage of the third phase input; D_(F) is the diodeconnected in parallel with the seventh switch; v_(ref) is a referencevoltage provided to the three-phase ac-ac matrix converter; i_(p) is apeak output resonance current of the three-phase ac-ac matrix converter;and v_(p) is a peak output resonance voltage of the three-phase ac-acmatrix converter.
 3. A three-phase ac-ac matrix converter for inductivepower transfer (IPT) systems comprising: a first line, a second line, athird line, and a fourth line, all of which are connected in parallel; afirst phase input connected to the first line, a second phase inputconnected to the second line, and a third phase input connected to thethird line; a first switch and a second switch connected in series onthe first line and on opposite sides of a first phase input connection;a third switch and a fourth switch connected in series on the secondline and on opposite sides of a second phase input connection; a fifthswitch and a sixth switch connected in series on the third line and onopposite sides of a third phase input connection; a seventh switch onthe fourth line; and a diode connected in parallel with the seventhswitch and on the fourth line, the seventh switch being directlyconnected to the first switch, the second switch, the third switch, thefourth switch, the fifth switch, and the sixth switch, the first switch,the second switch, the third switch, the fourth switch, the fifthswitch, and the sixth switch all being unidirectional, reverse blockingswitches, each including an IGBT or a MOSFET in series with a respectivediode, and the seventh switch being a bidirectional switch, and thethree-phase ac-ac matrix converter being configured to operate in apower regulation control mode according to rules in the following table:SWITCHING STATES IN DIFFERENT MODES OF OPERATION IN POWER REGULATIONCONTROL MODE. Output Power & Conducting Mode Resonant Current InputVoltages Switches 1 P_(out) < P_(ref), ip < 0 V_(b) < V_(c) < V_(a)S_(A1), S_(B2) 2 P_(out) < P_(ref), ip < 0 V_(c) < V_(b) < V_(a) S_(A1),S_(C2) 3 P_(out) < P_(ref), ip < 0 V_(a) < V_(c) < V_(b) S_(B1), S_(A2)4 P_(out) < P_(ref), ip < 0 V_(c) < V_(a) < V_(b) S_(B1), S_(C2) 5P_(out) < P_(ref), ip < 0 V_(b) < V_(a) < V_(c) S_(C1), S_(B2) 6 P_(out)< P_(ref), ip < 0 V_(a) < V_(b) < V_(c) S_(C1), S_(A2) 7 P_(out) >P_(ref), ip < 0 — D_(F) 8 ip >0 — S_(F,)

where: S_(A1) is the first switch; S_(A2) is the second switch; S_(B1)is the third switch; S_(B2) is the fourth switch; S_(C1) is the fifthswitch; S_(C2) is the sixth switch; S_(F) is the seventh switch; V_(a)is a first phase input voltage of the first phase input; V_(b) is asecond phase input voltage of the second phase input; V_(c) is a thirdphase input voltage of the third phase input; D_(F) is the diodeconnected in parallel with the seventh switch; P_(ref) is a referencepower provided to the three-phase ac-ac matrix converter; i_(p) is apeak output resonance current of the three-phase ac-ac matrix converter;and P_(out) is an output power of the three-phase ac-ac matrixconverter.